I expect that from a certain height, he would have reached a speed so high that he would have burnt when entering dense atmosphere?

Some meteoroids disintegrate when they reach the atmosphere, other don't... so I am not sure what would happen for a 100kg human+spacesuit.
Maybe he could jump from arbitrarily high? (notwithstanding digestion/food/drinks, gravity from other stars/planets, lifespan, cold)

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He "only" flew at the maximum speed of 370 m/s or so which is much less than the speed of the meteoroids – the latter hit the Earth by speeds between 11,000 and 70,000 m/s. So he was about 2 orders of magnitude slower. The friction is correspondingly lower for Baumgartner.

Note that even if he jumped from "infinity", he would only reach the escape velocity which is 11,200 m/s for the Earth, just like the slowest meteoroids. I guess that a good enough (and cooled) suit inspired by NASA rockets might be capable of protecting a human against such relative speeds even though for generic surfaces, they would almost certainly start to burn at the surface.

However, it wouldn't be pleasant to slow down from such speeds in the atmosphere. ;-) You see that if you uniformly slow down from 10 km/s to 0 km/s while flying through 10 km of the atmosphere, the penetration through the atmosphere takes about 2 seconds. However, getting from 10 km/s to 0 km/s in two seconds means that the deceleration is 5000 m/s/s or 500 $g$. I guess that not even he could survive that. ;-)